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A Multiresolution
Point Rendering
System
for Large Meshes
Szymon Rusinkiewicz & Marc Levoy
Stanford University
Edited by Ingrid
Introduction
• Trend in computer graphics towards using
sampled representations of real objects
during rendering
• Size of data meshes that can be scanned
is on the order of hundreds of millions of
points
• Scanned data has a large number of
verticies whose locations are often
imprecise due to noise
•Introduction
• Evidenced by increased use of 3D
scanners to produce three dimensional
sampled models of objects
• This is FAR beyond what is currently
displayable in real time
• Suggests an approach where individual
points are relatively unimportant
Introduction
• Examples of recent research employing
this paradigm
– Spline-fitting system by Krishnamurthy
and Levoy
– Range image merging system by
Curless and Levoy
– Octree particle rendering system by
Yemez and Schmitt
• These algorithms do not preserve the
original locations of the scanned points
What is QSplat?
• System for representing and progressively
displaying large scale meshes of scanned data
• Combines a multi resolution hierarchy based on
bounding spheres with a rendering system based
on points
• Does not preserve the connectivity of the
original mesh
• Intended to visualize scanned models that
contain significant amounts of fine detail at
scales near the scanning resolution
System Outline
• Preprocessing Algorithm
– generates hierarchy from triangular mesh
• Data Structure
– bounding spheres
• Node Structure
– sphere center, radius, normal, width of a
normal cone, (optionally) a color
• Rendering Algorithm
– visibility culling & drawing a splat
Preprocessing Algorithm
if (begin == end)
return Sphere(verticies[begin])
else
midpoint = PartitionLongestAxis(verticies[begin..end])
leftstree = BuildTree(verticies[begin..midpoint])
rightstree = BuildTree(verticies[midpoint+1..end])
return BoundingSphere(leftsubtree, rightsubtree)
Recurse down each subtree,
finding its bounding box
Bounding Box
of vertices
Preprocessing Algorithm
• Position and size of each bounding
sphere is encoded relative to its
parent and quantisized to 13 values
to save space
• Quantisized down the mesh, so
errors do not propagate
• Round up to ensure no holes
introduced by quantization
Creating the Data Structure
• Start with a triangle mesh produced
by aligning and integrating scans
[Curless 96]
Creating the Data Structure
• Place a sphere at each node, large
enough to touch neighbor spheres
Creating the Data Structure
• Build up hierarchy
QSplat Data Structure
• A single bounding sphere hierarchy
used for
– Hierarchical frustum and backface
culling
– Level of detail control
– Splat rendering [Westover 89]
QSplat Node Structure
Position
and
Radius
Tree
Structure
13 bits
3 bits
Normal
Width of
Cone of
Normals
Color
(Optional)
14 bits
2 bits
16 bits
6 bytes
QSplat Node Structure
Position
and
Radius
Tree
Structure
13 bits
3 bits
Normal
Width of
Cone of
Normals
Color
(Optional)
14 bits
2 bits
16 bits
• Position and radius encoded
relative to parent node
Center Offset
– Hierarchical coding vs. delta
coding along a path for vertex
positions
Radius Ratio
QSplat Node Structure
Position
and
Radius
Tree
Structure
13 bits
3 bits
Uncompressed
Normal
Width of
Cone of
Normals
Color
(Optional)
14 bits
2 bits
16 bits
QSplat Node Structure
Position
and
Radius
Tree
Structure
13 bits
3 bits
Delta Coding
[Deering 96]
Normal
Width of
Cone of
Normals
Color
(Optional)
14 bits
2 bits
16 bits
QSplat Node Structure
Position
and
Radius
Tree
Structure
13 bits
3 bits
Hierarchical
Coding
Normal
Width of
Cone of
Normals
Color
(Optional)
14 bits
2 bits
16 bits
QSplat Node Structure
Position
and
Radius
Tree
Structure
13 bits
3 bits
Normal
Width of
Cone of
Normals
Color
(Optional)
14 bits
2 bits
16 bits
• Number of children (0, 2, 3, or 4) – 2 bits
• Presence of grandchildren – 1 bit
QSplat Node Structure
Position
and
Radius
Tree
Structure
13 bits
3 bits
Normal
Width of
Cone of
Normals
Color
(Optional)
14 bits
2 bits
16 bits
• Normal quantized to grid
on faces of a cube
52526
QSplat Node Structure
Position
and
Radius
Tree
Structure
13 bits
3 bits
Normal
Width of
Cone of
Normals
Color
(Optional)
14 bits
2 bits
16 bits
• Each node contains bounding cone of
children’s normals
• Hierarchical backface culling [Kumar 96]
QSplat Node Structure
Position
and
Radius
Tree
Structure
13 bits
3 bits
Normal
Width of
Cone of
Normals
Color
(Optional)
14 bits
2 bits
16 bits
Viewer
Culled
Not Culled
QSplat Node Structure
Position
and
Radius
Tree
Structure
13 bits
3 bits
Normal
Width of
Cone of
Normals
Color
(Optional)
14 bits
2 bits
16 bits
• Per-vertex color is quantized 5-6-5 (R-G-B)
QSplat Rendering Algorithm
Hierarchical frustum /
backface culling
if (node not visible)
Skip this branch
Point rendering
else if (leaf node)
Level of detail
control
Draw a splat
else if (size on screen < threshold)
Draw a splat
else
Traverse children
Adjusted to maintain
desired frame rate
Rendering Algorithm
• Visibility Culling
– As recurse bounding spheres, cull nodes not
visible
– Backface culling
• if cone faces away, discard node & subtree
• If cone faces viewer, mark node no culling
• Frustum culling is performed by testing
each sphere against planes of the view
frustum
– discard nodes and subtrees that are outside
the view frustum
Rendering Algorithm
• Determining when to recurse
– Based on projected size of screen
– Node is subdivided if area of sphere when
projected on viewing plane exceeds a
threshold
– Adjusted frame to frame to maintain user
selected frame rate
• Type of data does not require smoothing
or complex frame rate adjustment
Frame Rate Control
• Feedback-driven frame rate control
– During motion: adjust recursion threshold
based on time to render previous frame
– On mouse up: redraw with progressively
smaller thresholds
– Consequence: frame rate may vary
• Alternative:
– Predictive control of detail [Funkhouser
93]
Tradeoffs of Splatting
• For rendering large 3D models, what are the
tradeoffs of:
Polygons
QSplat
Good for large, flat or
subtly curved regions
Good for models with
detail everywhere
Highly-efficient rasterization
with 3D graphics hardware
Higher per-pixel cost, but
less slowdown in
absence of 3D hardware
Decimation or creating
LOD data structures
is often expensive
Fast preprocessing
Demo – St. Matthew
• 3D scan of 2.7 meter
statue at 0.25 mm
• 102,868,637 points
• File size: 644 MB
• Preprocessing time: 1
hour
• Demo on laptop (PII 366, 128
MB), no 3D graphics hardware
Future Work
• Splats as primitive
– Unify rendering of meshes, volumes, point
clouds
– Compatible with shading after rasterization
– Hybrid point/polygon systems
• High-level visibility / LOD frameworks
– Store different kinds of data at each node:
alpha, BRDF, scattering function, etc.
– Potentially could be used to unify imagebased-rendering (IBR) techniques
Acknowledgments
• Thanks to Gary King, Dave Koller,
Jonathan Shade, Matt Ginzton, Kari Pulli,
Lucas Pereira, James Davis, and the
whole DMich gang
• Digital Michelangelo Project sponsored
by Stanford University, Interval Research
Corporation, and the Paul Allen
Foundation for the Arts
QSplat Downloads
• QSplat binaries and source code
http://graphics.stanford.edu/software/qsplat
• Digital Michelangelo Project archive at
http://graphics.stanford.edu/projects/mich